Four-Dimensional Semi-Riemannian Szabó Manifolds
In this paper, we prove that the deformed Riemannian extension of any affine Szabó manifold is a Szabó pseudo-Riemannian metric and vice versa. We prove that the Ricci tensor of an affine surface is skew-symmetric and nonzero everywhere if and only if the affine surface is Szabó. We also find the ne...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/6663361 |
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| author | Abdoul Salam Diallo Punam Gupta |
| author_facet | Abdoul Salam Diallo Punam Gupta |
| author_sort | Abdoul Salam Diallo |
| collection | DOAJ |
| description | In this paper, we prove that the deformed Riemannian extension of any affine Szabó manifold is a Szabó pseudo-Riemannian metric and vice versa. We prove that the Ricci tensor of an affine surface is skew-symmetric and nonzero everywhere if and only if the affine surface is Szabó. We also find the necessary and sufficient condition for the affine Szabó surface to be recurrent. We prove that, for an affine Szabó recurrent surface, the recurrence covector of a recurrence tensor is not locally a gradient. |
| format | Article |
| id | doaj-art-567b9d88b8e64d7c83add69e63dc1afe |
| institution | DOAJ |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-567b9d88b8e64d7c83add69e63dc1afe2025-08-20T03:20:20ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/66633616663361Four-Dimensional Semi-Riemannian Szabó ManifoldsAbdoul Salam Diallo0Punam Gupta1Université Alioune Diop de Bambey, UFR SATIC, Département de Mathématiques, Equipe de Recherche en Analyse Non Linéaire et Géométrie, B. P. 30, Bambey, SenegalDepartment of Mathematics & Statistics, School of Mathematical & Physical Sciences, Dr. Harisingh Gour University, Sagar 470003, Madhya Prades, IndiaIn this paper, we prove that the deformed Riemannian extension of any affine Szabó manifold is a Szabó pseudo-Riemannian metric and vice versa. We prove that the Ricci tensor of an affine surface is skew-symmetric and nonzero everywhere if and only if the affine surface is Szabó. We also find the necessary and sufficient condition for the affine Szabó surface to be recurrent. We prove that, for an affine Szabó recurrent surface, the recurrence covector of a recurrence tensor is not locally a gradient.http://dx.doi.org/10.1155/2020/6663361 |
| spellingShingle | Abdoul Salam Diallo Punam Gupta Four-Dimensional Semi-Riemannian Szabó Manifolds Journal of Mathematics |
| title | Four-Dimensional Semi-Riemannian Szabó Manifolds |
| title_full | Four-Dimensional Semi-Riemannian Szabó Manifolds |
| title_fullStr | Four-Dimensional Semi-Riemannian Szabó Manifolds |
| title_full_unstemmed | Four-Dimensional Semi-Riemannian Szabó Manifolds |
| title_short | Four-Dimensional Semi-Riemannian Szabó Manifolds |
| title_sort | four dimensional semi riemannian szabo manifolds |
| url | http://dx.doi.org/10.1155/2020/6663361 |
| work_keys_str_mv | AT abdoulsalamdiallo fourdimensionalsemiriemannianszabomanifolds AT punamgupta fourdimensionalsemiriemannianszabomanifolds |